Question 1029569: Please help me solve the following problem about ellipses. Find the standard form of the equation of the ellipse with the given characteristics and the center at the origin. Vertical major axis; passes through points (4,0) and (0,2). Sure, it says passes through, but how can you be sure that those are the "endpoints" of the ellipse, or that they represent "a" and "b"?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Please help me solve the following problem about ellipses. Find the standard form of the equation of the ellipse with the given characteristics and the center at the origin. Vertical major axis; passes through points (4,0) and (0,2). Sure, it says passes through, but how can you be sure that those are the "endpoints" of the ellipse, or that they represent "a" and "b"?
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Because of symmetry, if the center is at (0,0), and the major
axis is vertical, (0,2) and (0,-2) must be vertex points,
and (4,0) with (-4,0) must be vertex points.
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But that implies the vertical axis has length 4
and the horizontal axis has length 8.
And that implies that the horizontal axis is the major axis.
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Did you post your problem correctly?
Cheers,
Stan H.
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